Cutting into the meat of social mechanics, it is more about circumstance and consequence. There are many strategies in dealing with people; it gets more complicated when there is deceptions and it is more about ancillary benefits.
Strangely everything boils down to a "cliche" that people want to be wanted for themselves. The funny thing about the "cliche" is that "themselves" is nothing simple and very often complicated. The only times a relationship becomes very simple is that it is transactional/economic or when there is a deep connection.
Skills are necessary to avoid Noise. What I mean by noise is the information and communication theory definitions of it . Noise is both uncertainty and the natural messy nature of how we communicate as humans. A simple instruction being a feat of abstract thinking, having a precise set of expectation, and a feat of probabilistic interpretations. (the lessons taught in TTC effective communication is more pronounced when we learning a new language, when we hear one that has a set of sounds Culturally/Linguistically we cannot hear like the 5 tones in Chinese)
Where skills are heaviest and most useful is in reducing noise is Analysis and Information Gathering. Where skills are least is in delivery and for those who have mastered all the fundamentals (delivery and information gathering) there are route techniques and tricks.
Psychology is one of the key skills, but most interestingly such a broad topic. there is Psychology the science we learn, and the one we experience and have observed. Depending on the lense we have cogntively psychology is influenced by Background Culture, our Professional Culture, and the social skill sets we need to survive.
It is interesting to measure one's life by transactional vs non-transactional but positive relationship we have.
Simplifying Social Mechanics without getting deep into a Philosophical Discussion is the challenge, because you trim the discussion by removing the examples and supporting statements to the theory proposed.
It is also assumes that you have a similar experience with the reader. I like Steve Longs comment in an interview, which is to the effect Hero is not for Assholes. I think anything written is universally not meant to be interpreted by the kind of people who seek to "strawman" the writer's own words. I've read Dawkin's: The greatest show on earth and the language is so precise and protectionist it turned off my wife from reading it; I didn't mind it because I knew it was designed to limit the wiggle room for assholes.
I talk about leverage in my Social Mechanic rules. I don't mean for Leverage to be a mechanic, but one of my intentions is to provide a creative commons description of the real world modeled in games so that people have a better mental model and that people with better wording can improve on it and spread it around. It the mental model gives people not only a tool for an RPG but a better understanding of relationship Huzzah!